Celebration of Scholars
Ecological Interactions: an Application of Differential Equations
Name:
Marquell Williams
Major: Economics, Math
Hometown: Rockford, Illinois
Faculty Sponsor: Haley Yaple
Other Sponsors:
Type of research: Course project
Abstract
Ecological interactions are encounters and the resulting effects between different organisms within the same community, or the symbiotic relationships between Earth’s inhabitants. Few species live in isolation, and even fewer exhibit population growth patterns that do not involve interactions with other organisms. These ecological interactions are important as they determine Earth's biodiversity. We study three pairs of coupled differential equations involving three organisms in order to measure and predict changes in the aquatic ecosystem. The predator-prey, competition, and cooperation models of ecological interactions, collectively called the Kolmogorov models, offer accurate qualitative insight into population growth for many species. While these models predict population growth, analysis using differential equations allows for the determination of relative population changes in an ecosystem over time, and natural equilibrium points as a result of environmental factors and symbiotic relationships. Numerical solutions and analytical qualitative analysis are utilized to measure and predict changes within an ecosystem.
Submit date: March 18, 2019, 1:39 p.m.